International
Tables for Crystallography Volume A Space-group symmetry Edited by Th. Hahn © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A. ch. 9.1, p. 749
Section 9.1.9. Example
a
Universität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany |
This example is discussed in Azároff & Buerger (1958, pp. 176–180).
The lattice parameters are given as ,
,
,
,
,
. The scalar products resulting from these data are given in Table 9.1.9.1
. The scalar product
is positive. Thus the transformation
is applied. The new scalar products are all non-positive as given in the second row of Table 9.1.9.1
(within the accuracy of the experimental data). Comparison with Table 9.1.8.1
leads to M6, Voronoi type IV and the monoclinic Bravais lattice mP.
|
The transformation related to this case leads to a monoclinic conventional cell but does not consider the possibility of shorter basis vectors. For this reason, it is necessary here to look at the other vectors of the set V in the () plane, the only one of interest is
. The length of this vector is
, which is shorter than
(
) and leads to the cell parameters
.
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